Methods of permanently elongating strip

ABSTRACT

A STRIP IS PERMANTENTLY ELONGATED BY APPLYING A TENSION FORCE TO IT AND CONSTRAINING IT WHILE UNDER TENSION TO AT LEAST ONE BEND AND AT LEAST ONE BEND REVERSAL WHICH CAUSES YIELDING AND AN INCREMENTAL ELONGATION STRAIN THAT IS PRODUCED BETWEEN A BEND AND A SUBSEQUENT BEND REVERSAL IN WHICH THE MAGNITUDE OF INCREMENTAL ELONGATION STRAIN IS RELATED TO THE APPLIED TENSION FORCE AND APPLIED BENDING STRAINS.

Jan, 5, 1971 Filed Feb. 28, 1968 Fi g.l.

Siress- Strain Diagram M. G. KINNAVY I METHODS'OF PERMANENTLY ELNGATING s'TR'IP 3 Sheets-Sheet 1 Fig.2.

Sirain Distribution Siress Disiribr. ion

' ldealized Stress-Strain Diagram Yield Paint /QANork Hardening. I b

| 3 5 E) w I 7 Elost'c g Perfectly Plasiic 1 ar 6 4 o Strain T 6 0' m Strain k'R| I4R2+ y flty Strip Surface I Flg o I Yield on Tension I I 1%"! 2 Sude of S'mp Yield rYield Z I Strain E if I Stress T 2 r t Middle Fiber g, l Q 1 2s 2 2 Nepiral l" A F'ber 2 "If 2 Neutral Fiber fi 2 1 J 0/ 6 Strip Surface I Stress r isfribufion ly Disribufion I I I f +fit I I o Fig .4. y a 2 Yield on Both I 8 Sides of sm l" 2 T 7 "2' Z i I t lfi 2 E F i fi- -l I INVENTOR o A 2 0) Martin G. 'Kinnavy g4Z/ wa Jam 5, 19 I M. G. KINNAVY 3,552,175

mmnons OF PERMANENTLY ELONGATING smr Filed Feb. 23, 1968 3 Sheets-Sheet, e

.5. Strip Elongation Upon Bending Strain Reversal i \l r'i 53. 5% 2 g I X if; "22 X Strain Middle Fiber Stress flie i ran %?i fan 9 4,89 2 0 Q V 21 Case 11 i i I Strip Elongation Upon Bending Strain Reversal y-{we i am 5 6* 0*: o --a ylzflflf I2 0 J I 2 I i 2 F 2 fl (an? r. ED- U- n] Strain Middle Fiber 5 i $tre ss l p =1.so

o CaseI I .7. Graph Showing Different Regions of Elongation 8 Bending Strain Parameters.

mvmron Martin G. Kinnavy 6 (Bending Stain Parameter) 66 (Initial Elongation Strain Parameter) j 5 1971 M -|(||\|NAVY- 3,552,175

'mmcmo'os 0F PERMANEN'ILY :ELONGATING scum-r 3 Sheets-Sheet 5 Filed Feb. 28, 1968 Building "Col.

Hydraulic Cyl.

Martin G. Kinnuvy United States Patent ABSTRACT OF THE DISCLOSURE A strip is permanently elongated by applying a tension force to it and constraining it while under tension to at least one bend and at least one bend reversal which causes yielding and an incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental elongation strain is related to the applied tension force and the applied bending strains.

This invention relates to a method of permanently elongating strip material to remove irregularities in shape 1 and to modify physical properties or structure. 1

I. PROBLEM PRESENTED TO THE INVENTOR The manufacture of metal strip leaves irregularities A common problem in the production of continuous metal strip is the irregularity of shape in the form ofwavy edges and bubbles between the edges. For many applications, material. with such irregularities is neither saleable nor useable. These irregularities commonly appear in strip produced by established methods and modification of those methods is either not feasible or. too-costly.

The, problem of :strip irregularities, therefore must be solved in operations subsequent to the basic strip production. operations. II. PRIOR ART Stretching process to remove irregularities in metal strip one of the earliest methods for removing irregularities from strip or plate was the simplejaw stretch leveler which dates back to the nineteenth century. If one considers that a metal strip is composed of a plurality of metal fibers running in a plane in the longitudinal direction of a metal strip, then in the case of an elastic-perfectly plastic material, pure stretching with the longest fiber elongated into the yield zone will produce leveled strip; see definitions of leveled strip infra. If on the other hand the same strains are applied to a materialwhich work-hardens, a somewhat different effect takes place. Fibers which were short will remain short fibers in the stretch-leveled strip. The reasonfor this is that after all the fibers were strained to the same length with each fiber undergoing a different individual strain, the more highly strained material recovered a greater amount upon unloading. Thus the strip condition is only partially corrected. The consequence of this vis that pure stretch leveling (see definition of leveling infra) ice works best on materials which work-harden only to a slight degree; that is, to materials which are nearly elastic-perfectly plastic. For this class of materials, however, stretch leveling is a very easily controlled process in that the only requirement is that the longest fiber be strained to at least the yield point. In view of the necessity to strain the shortest fibers well into the yield zone, the process of stretch leveling is not useful for materials in which the ultimate tensile strain is only nominally higher than the yield strain.

Simple jaw stretcher leveling is applicable only to the stretching of material in sheet form and not to a continuous process. Nevertheless, the idea of simple stretching has been applied to stretching of strip continuously. In this process the essential components are a drag bridle, a drive bridle, a suitably powered mechanical drive system, and the associated controls. While this process, at first glance, embodies the simplicity of the simple jaw stretcher, close examination discloses serious, but not obvious, weaknesses:

(1) It is necessary with continuous stretcher leveling, to provide sufiicient tension capability in the power transmission system to produce the full yield tension in any material to be processed. This high tension requirement imposes the requirement of large expensive drive systems.

(2) Basic kinematic analysis of the bridle-strip system shows that almost all of the strip elongation produced in the process must take place while the strip is in contact with the highest tension drag bridle roll. The consequence of this is that the roll covering, usually an elastomeric material, has an abbreviated life. Furthermore, because the strip approaches this roll while still in the elastic stress range and leaves the roll when in the plastic stress range after having been extended an arbitrary amount, there is large unavoidable velocity mismatch between the strip and the roll covering.

(3) In many systems, it has been common to connect the mechanical drive systems of the drag bridle system to the drive bridle system. The reason for this is to eliminate electrical motors and generators. This cost saving, however, is not without penalty. In a completely geared system one has no control over the distribution of the torque supplied to each drive and drag 'bridle roll because loads and torques always follow the stifiest possible paths. As a result of this, the manufacturers of this equipment have no control of torque distribution. The problem is further complicated by roll cover wear to the extent that even if only one cover wears, all roll covers must be reground. Furthermore, because any bridle roll will change tension, the strain in the strip is correspondingly changed, and thereby produces an additional source of small velocity mismatch which effect cannot (in these systems) be minimized by adjustment of individual motor or generator units.

Roller leveling process Another well-known method to level strip is the roller leveling process. This process is applicable to sheet leveling and to continuous strip leveling. It consists of passing the material between two sets of rolls placed relative to each other so that the strip is constrained to a tortuous path, thereby causing flexing of the material in alternate directions. This process is known to level strip. Generally, the Work rolls are small in diameter and tend to diminish in size as the strip thickness to be processed is decreased. For example, one manufacturer uses inch diameter rolls for a thickness range of 0.010 inch to 0.050 inch and 1% inch diameter rolls for a thickness range of .015 inch to .064 inch. The use of small work rolls has necessitated that other sets of rolls of approximately twice the diameter of the work rolls be used in support of the work rolls to prevent excessive deflection; hence the so-called four-high leveler consists of two sets of work rolls plus two sets of backup rolls to support the work rolls.

In recent times, even four-high machines have had to become six-high machines because of the deflection problems, While backup rollers and backup rollers for backup rollers have, to a large degree, surmounted the deflection problems, they have introduced a whole new array of process deficiencies. One of the more serious defects is the so-called stripping problema direct effect of the backup roll. Another very serious defect is the control problem. It has been common practice to design into roller levelers vertical adjustability of the backup roll system so that tight portions of the strip might be subjected to more work in the process while loose portions of the strip are subjected to less working.

Roller levelers are of two types, driven and non-driven or pull-through. A serious defect associated with the former type is the strip marking caused by the velocity mismatch between the strip and the driven rolls. The velocity mismatch arises as the strip is elongated in the process, and for which no provision is readily made in the roller drive system. Attempts to overcome this operational defect have been made by using adjustable slip clutches in the drive systems, as well as by resorting to other nonpositive drive means, e.g. hydraulic drives.

The roller leveler with a skilled operator at the controls can produce acceptable strip from an appearance point of view. However, in many cases, leveled strip is subsequently slit into narrower coils. Because of the differential working of the rolls against the strip, different residual stress patterns exist across the width of the strip. Because of these differential residual stresses, there appears in the plane of the strip another system of stresses which when disturbed by a slitting operation produces objectionable edge bow in the slit coils. To overcome some of the limitations of roller leveling, many machine builders have incorporated tension bridles to the roller leveling process, This has produced an improved product and has allowed the processors to handle strip of lighter gauge than could be leveled without tension.

A well-known process which uses high tension bridles is the Compagnie des Ateliers et Forges de la Loire (C.A.F.L. Process). Another tension roller leveling process known as the BNF process is described in Research Report A1241, dated June 1969 of the British Non-Ferrous Metals Research Association entitled, The Elimination of Edge Bow in Slit Strip.

Shortcomings of the prior art While all of the foregoing approaches to the leveling process have had varying degrees of success, there remains with all of them serious drawbacks. In every instance in which work rolls are used for the purpose of flexing the strip, that is, in the roller leveling process, the tension roller leveling process, the C.A.F.L. process, and the BNF process, the work rolls are invariably small in diameter and require the use of backup rolls. With small work roll diameters, operating speeds are low, the design is complex because of the need for backup rolls, and there are greater wear and maintenance problems associated with frequent dressing of the work rolls and frequent work roll changes. Furthermore, the use of a backup roll system frequently causes strip marking,

III. THE INVENTION PRESENTS A NEW AP- PROACH TO THE ELONGATION OF STRIP MA- TERIAL The present invention is a new process of permanently elongating metal strip. This can be used to remove strip irregularities or to modify the physical properties of the strip among other uses. For any given set of physical properties of the strip material, one can assign combinations of tension and bending radii such that the desired strip elongation will be produced, and the desired effects, including levelng and modification of physical properties will result. It is possible that an arbitrary combination of tension and bending will produce some elongation. These arbitrary combinations, however, of tension and bending will not produce the result sought whereas the new process will produce the desired result with great accuracy.

Use of the new process avoids major equipment problems encountered in the present methods (prior art) for elongating strip. The advantages of the new process are: low maintenance of equipment, low downtime of equipment, no strip marking caused by the differential velocity between driven rolls and strip, prolonged life of bridle roll covering, relatively low tension requirements, simplicity of control, ease of operation, and no restrictive speed limit. Furthermore because the new process relates tension with radius of curvature of bending in a prescribed manner, one is able to optimize tensions and roll diameter combinations to achieve the desired result. By doing this one is no longer limited to the use of small diameter rolls. This can eliminate the design complexity of a backup roll system as well as the operational difliculties associated with such systems including but not limited to strip marking.

Definitions (1) Leveling.Leveling is a process by which shape irregularities in metal strip are removed so that the strip appears uniform. Leveling removes wrinkles from strip but not gross irregularities such as coil set or roll set (defined infra). Leveling makes all fibers of equal length in any given plane. The fibers, however, may vary in length from plane to plane throughout the thickness and the strip will still be leveled. The strip may have roll set or coil set and still be leveled.

(2) Leveled strip.If an area of metal strip without roll or coil set were laid upon a flat table and its surface conformed everywhere with the surface of the table, it would be considered as flat or leveled strip. Irregular strip laid upon a flat table would not be everywhere in contact with the surface of the table. In this case some fibers would be longer than other fibers.

(3) Coil set or roll set.--A distinction must be made between local strip irregularities removable in a leveling process and the strip condition known as roll or coil set. If a length of strip assumes a longitudinal curvature when it is free of restraint, it is said to have roll or coil set. It is possible for a length of strip to have roll set with or without irregularities. Strip with roll or coil set, but without irregularities, is considered herein to be leveled strip. A simple multi-roll flattener can remove coil set from strip, but it generally is incapable of removing strip irregularities. If one considers strip to be comprised of a multitudinous array of fibers, each fiber in flat and leveled strip wil have the same length. Strip with coil or roll set will correspond to a linear variation of fiber length throughout the thickness of the strip. If this pattern of variation is identical in a transverse direction, the strip is said to be leveled. If this variation changes in a transverse direction, the strip would have shape irregularities in addition to roll or coil set. Coil or roll set is related to what is called transverse bow by Poissons Ratio, a physical property of the strip.

I provide a method of permanently elongating strip which comprises, applying a tension force to the strip, and constraining the strip while under tension to at least one bend and at least one bend reversal which causes yielding and an incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental elongation strain is related to the applied tension force such that when the yielding occurs on alternate sides of the strip on succes sive bends the increment of elongation strain follows the equation r-l- R2 Ae 2tey I provide a method of permanently elongating strip which comprises, applying a tension force to the strip, and constraining the strip while under tension to at least one bend and at least one bend reversal which causes yielding and an incremental elongation strain that is produced between a bendand a subsequent bend reversal in which the magnitude of incremental elongation strain is related to the applied tension force .such thatwhen yielding occurs on at least oneside of the strip at a bend and on both sides of the strip at the subsequent bend reversal the increment of elongation strain follows the equation in which Other details, objects and advantages of the invention will become apparent as the'following description of' a present preferred proceeds.

.In the accompanying drawings I have illustrated a present preferred method-of-practicingthe invention in which: v a a :FIGgl is a stress-strain diagram; FIG. 2 is an idealized stress-strain diagram;

FIG. 3 is a diagram showing yielding on tension side of the stripknown as Case I;

FIG. 4 is a diagram showing yielding on'both tension and compression sides of the strip-known as Case II; FIG. 5 is a diagram of strip-elongation upon bending strain reversalCase II;

FIG. ,6 is a diagram of strip elongation upon bending strain reversal-Case I;

method of practicing the invention -FIG. 7 is a diagram showing different regions of" elongation and bending strain parameters;

FIG; 8 is a schematic diagram: of app'aratusused in examples of, application. of method to strip 'material;

and

3 FIG.9.- is atable -showing'. incremental elongation strain for Case. IA, Case IB and Case II. 1' C Elongation-of strip-is related to leveling. This relationship can be shown by referring to an idealized stressstrain diagram for an elastic perfectly plastic material as shown in FIG. 1. Consider, for example, irregular strip free of coil set. If. the strip is irregular, it has bubbles or waves and there will be a difference in fiber length. If a length 'of suchstrip iselonga'ted, the short fibers" will be loaded in tension fi'rstQAs the elongation increases, longer fibers will begin to share the tension load. If the elongation is further continued until the longest fiber is strained beyond the yield point, the shortest fiber will be strained to,an even greater magnitude. However, each fiber so elongated will have the same stress. This is illus-. trated in FIG. 1 in which Point 1 shows the stress and strain for the longest fiber, and Point 2 shows the stress and strain for the shortest fiber. Now, if the strip is unloaded, each fiber will relax the same amount because the path of the stress-strain points is parallel to the initial elastic loading curve. This means that recovery strain R is equal to recovery strain R Thus the final condition of the strip will be such that every fiber has the same length and the strip is said to be leveled.

Consider a material in which work-hardening takes place after the yield point is reached. If such a material is elongated in a similar way, we will produce stressstrain Points 3 and 4, as shown. Now, if the load is relaxed, it can be seen that the recovery strain for the longest fiber R is less than the recovery strain for the shortest fiber R In this case the strip condition, although it can be improved, can only be partially corrected. Thus leveling by means of stretching or elongating the material works best on materials which do not exhibit a high degree of work-hardening. For materials with little or no work-hardening, leveling through stretching is a very easily controlled process in that the only requirement is that the longest fiber be strained at least to the yield point. Thus the problem of leveling becomes the establishment of a suitable mechanical process whereby all fibers of the strip are stretched beyond the yield point. The amount of stretch or elongation necessary to level strip depends upon the initial fiber length variation throughout the strip.

In the bending of strip, straight lines in an unloaded, unstrained strip will remain straight upon the deflection which accompanies the application of loads. These straight lines, however, will become inclined toward each other. The consequence of this is that some fibers of the strip Will elongate with respect to other fibers of the strip, and the relative elongation will be proportional to the distance from the unstrained fiber; that is, the fiber strain is proportional to the distance from the unstrained,

= yield stress. The yield strains in both tension and compression have also been taken as equal. If tension is applied to a fiber, it will be accompanied by a strain such that all stress-strain points will lie upon the straight line 0-1 until the yield stress is reached. Thereafter, as the strain is increased, the stress will remain the same and all stress-strain points after yielding will lie upon the line 1-5. 1

If a, fiber has been strained such that its stress and strain are given by Point 3 in FIG. 2, a further increase in strain produces no increase in stress. On the other hand, if the strain at Point 3 is reduced, the stress will decrease so that all stress-strain points upon continued decreasing strain will lie along the line 3-4 which line is parallel to the initial elastic stress-strain line. Thus Point 4 may have a positive strain and a negative or compressive stress. If a further strain decrease takes place, the stress-strain path will continue leftward along the line defined by 26. Thus, with the model shown, it is possible to develop an infinite number of continuous stress-strain paths bound by extensions of the tensile yield stress line 1-5 and the compressive yield-stress line 2-6. Any stress-strain path from one of these lines to the other will always be parallel to the initial elastic curve.

Consider typical linear strain distributions and their associated stress distributions through the strip thickness. It is, necessary to distinguish between stress distributions in which the yield stress appears on either one or both sides of the strip. If the yield stress is reached in tension alone, this is a Case I stress distribution. If the yield stress value is reached on both tension and compression sides of the strip, it is called a Case II stress distribution. Refer to FIGS. 3 and 4.

As a consequence of the linear strain distribution, any strain distribution may be considered to consist of an elongation component and a bending component. The elongation component is the strain that exists at the middle of the strip; the bending component is zero at the middle of the strip and is maximum at the surface of the strip. Strain componentsare designated in terms of the yield strain ey. Thus as) is the extension component of the strain and [Sky is the bending component of the strain. Two strain distributions are shown on the lefthand sides of FIGS. 3 and 4 in which the vertical line is taken as the zero strain axis, and strains to the right of this line are taken as tension strains.

The stress distributions corresponding to these strain distributions are obtained by utilizing the stress-strain diagram, FIG. 2, together with the strain distributions shown. These stress distributions are shown at the righthand sides of FIGS. 3 and 4. The force per unit Width of strip corresponding to the Case I stress distribution will be given by A similar calculation for the Case II stress distribution will show that the tension force per unit width of the strip will be given by The geometrical relation between bending strain and curvature is given by where R is the radius of curvature of the neutral fiber of the strip.

With these established preliminary considerations, the strip subjected to tension in combination with a bending strain will be examined when it is subjected to a reversal of the bending strain when the combination of tension and bending strains lies within the teaching of this invention.

FIG. 5 shows a strain distribution by means of the line at the left side of the figure, this line labeled 1. The surfaces of the strip are indicated by the horizontal lines at the top and bottom of the figure and the middle fiber of the strip is so labeled. The initial strain distribution is made up of the extension or elongation strain component, aey=1.25 5y and the bending strain component, pey=2.50ey. The stress distribution which corresponds to this strain distribution is obtained through use of the stress-strain diagram FIG. 2, and is shown at the right of FIG. 5 by the series of straight lines 11*110. This stress distribution is in equilibrium with the force per unit width of strip F ayt.

Now upon reversal of the bending strain component, the slope of the strain distribution is simply reversed but since the applied load remains the same the new stress distribution must be in equilibrium with the same force; namely, F=0.5 lTyt. The constraints of the stress-strain relations described earlier and illustrated in FIG. 2 must be followed. The only strain distribution that has the prescribed bending strain component that obeys the stressstrain constraints described, and that transforms the initial stress distribution into a new stress distribution in equilibrium with the applied tension force, is the strain distribution labeled 2. The new stress distribution is given by 0222*-2-0. Upon inspection one will see that a point L i o'yt 2 above the middle fiber, a strain change of 6y occurs, while at Point 2* no strain change occurs. Point 2* is located at a distance l i ayt 2 2B 2 above the middle fiber. It now follows directly from geometry that the increment of elongation strain of the middle fiber, Ae is Use of the earlier stated geometrical relation between bending strain, strip thickness, and radius of curvature in this equation yields a more useful expression for the incremental strain produced during bending strain reversal under maintained tension, namely,

From this equation an expression for force required to produce a given increment of elongation strain may be obtained, namely,

F Rayey 5 1) It is of significance that the increment of elongation strain is independent of strip thickness. This result is of utmost importance. However, as the material thickness is reduced, a given tension force causes increasing stresses. The particular case of strip thickness approaching zero indicates a tendency toward infinite stresses which cannot exist. The explanation of this apparent anomaly lies in the range of validity of the above expression. A condition that must be met for this expression to apply is E 1 t cry! or equivalently The above teaching was directed to the case of a stress distribution which has been designated a Case II stress distribution. The effect of a bending strain reversal when a Case I stress distribution exists in the strip will now be considered. In FIG. 6 a selected extension strain component of aey=1.25 ey and a bending strain component of fley=l.50 ey are used.

The reversal of the bending strain must be accomplished within the same constraints as before. In this case, it can be observed that the stress change at the surface initially at the tesnion yield stress is F ar /2s (1 and that the stress and strain remain unchanged at a point a distance above the middle fiber given by The strain change at the surface initially strained above the yield strain in tension is From geometry, the incremental elongation strain of the middle fiber is c which upon use of the earlier shown expression for bending strain becomes t 415 F -[YW (Wall This expression is valid for all surface strain changes given by the. increments of elongation strains produced during bend-- in'g'strain' reversals are 10 tical problems. With the substitution of these variables in the expression above, we have In the equation Roy (7+ 1) E the above limitation on a imposes a restriction on namely, 20.5.

Similarly for simple Case I stress distributions to transform into simple Case I stress distributions upon the reversal of the bending strain, hereafter called a Case IA stress distribution, the requirement is (Case IA) In some cases, a simple Case I stress distribution is transformed into a simple Case II stress distribution, hereafter called a Case IB stress distribution, and the condition for this is that (Case IE) or equivalently,

3 F a 2R ryey (Case II) The above conditions have been illustrated graphically in FIG. 7. We have shown that for both Case II and Case IA the increment of elongation strain described The stress distributions 'at-a benda'nd at a bend reversal falling within the teachinglof this invention are simple, that is, the only stresses below the yield stress in magniq. tude are confined to a region of the strip thickness and the stresses in thisregionvary linearly and continuously from the maximum tension value to the maximum compression value. All stress distributions, however, that :pre-F" vail between a given bend and a subsequent bend reversal are not simple. But within the teaching herein, the process relates to the extensio'mof strip that occurs while subjectedtqa tension force from a simple. stress distribution which is associated with a bending strain, to a subsequent simple stress distribution, which is associated with a bending strain of opposite sign; In these instances the previous strain history will not be evident in the stress distribution; however the slope oil -the. elastic portion ofthef stress dis.- tribution will not bethe same as the slope of the strain. distribution.

In order that stress distributions of the Case II type remain simple, it is necessary that Point 2* in FIG, 5 be. above Point 1*. For this tobe so i i Tl/25.51 Elias-been-found convenient tense the variables a and- 3- describedaearlier-in.theapplication of the method'to pracf earlier is given by and that for Case I-A the increment of elongation strain is given by /i l Rey Rey 1 ayt 8y or equivalently,

column. Bending strains were applied by means of rolls can The inventioincan alsovbe understood by practical applications of the method to strip material under certain conditions as shown by the following examples. The apparatus (referring to FIG. 8) used in these examples consisted essentially of a means to apply a tension force to the strip and a means to produce bending strains and bending strain reversals. The means of applying tension force was a hydraulic cylinder which was connected to a force 'gag'e which was connected to one end of the strip. The other end of the strip was connected to a force gage which was connected by a bracket to a fixed building carried on a cart riding on a smooth track. A hydraulic power supply was used to provide a ---source of hydraulic pressure for the hydraulic cylinder. Strip 'was threaded over and under the rolls mounted on the cart and clamped as shown in FIG. 8. The hydraulic cylinder is used to remove slack from the strip; then a gage length is marked on the strip (50 inches). A suitable tension force is then applied to the strip by means of the hydraulic cylinder, the magnitude of the tension force being measured'by means of load cells. The cart is then moved along the length of the strip, thereby subjecting the strip to an initial bending strain distribution; then to a bending strain reversal; then to a second bending strain reversal. The distance between the gage marks 1 1 is measured after the passage of the cart along the strip and this measurement is compared with the original gage length. This comparison then yields the strip elongation; that is,

final lengthinitial length initial length EXAMPLE 1 Material: Aluminum, 3105H25 Thickness: t, 00319 in. (measured) Yield stress: ay, 26,600 lb./in.

Modulus of elasticity: E, 8,520,000 lb./in. Yield strain: ey, 0.00312 Yield tension: ayt, 850 lb./ in. of width The diameter of the rolls on the cart was 6 inches; thus the bending strain parameter is calculated as follows:

t (0.0319 ims 6.0319

In this example, a tension force of approximately 75 percent of the yield tension was used; i.e., F=637.5 lb./in. of strip width. To establish which Case in FIG. 7 is applicable, Table I (FIG. 9) has been developed. Thus,

percent elongation: X 100 which shows a Case IA situation.

First a is computed from the force equation. Thus,

F (x- 1+,B-- \/4fl (1ayt Substitution of numerical values gives The increment of elongation strain is then F Ae-[2fl 8fl 1 J ]ey Ae=[(2) 1.095 s (1.695) (0.25)]=1.55ey

In the example fixture the initial bending strain is followed by two bending strain reversals. Thus from the initial bend there is a middle fiber strain of aey=l.39ey and from the two bending strain reversals, two increments of strain each of magnitude Ae=1.55ey to produce a total elongation strain of The example result showed that with a gage length of 50 inches an elongation of 0.782 inch was produced, which corresponds to a strain of The difference is 0.015640.0140 or 0.00164 or 10.5%.

EXAMPLE 2 Material: Aluminun, 5052H32 Thickness: t, 0.040 inch Yield stress: uy, 27,600 lb./in.

Modulus of elasticity: E, 9,550,000 lb./in.-"- Yield strain: ey, 0.00288 Yield tension: ayt, 1105 lb./ in. of width In this test the bending strain parameter is 12 With an applied tension force of F :857 lb./in. of width,

and

The quantity 1/25 is 0.2175 which means a Case IB situation. Thus a is computed as follows:

The increment of elongation strain upon bending strain reversal is Rayey (3.02) (27600) (.00288) =2.57ey

The total elongation strain is obtained as before The test result showed an elongation strain of 0.0222. The difference is 0.0006 or 2.7%.

EXAMPLE 3 Material: Aluminum, 5052H32 Thickness: t, 0.0512 inch Yield stress: 0y 24,700 lb./in.

Modulus of elasticity: E, 8,970,000 lb./in. Yield strain: 5y, 0.00276 Yield tension: ayt, 1263 lb./in. of width ilthfollows from Table I that we have a Case II situation.

F oz= -y 3: (0.517) (3.06) 1.58

and the increment of elongation strain upon bending strain reversal is Ae= (2oc1)ey=2.16ey' The total elongation strain is then e=[l. 8+(2) (2.l6)](.00276) The observed elongation strain in the experiment was 0.0164 which is different by only 0.6 percent.

While I have shown and described a present preferred embodiment of the invention and have illustrated present preferred methods of practicing the same, it is to be distinctly understood that the invention is not limited there-.

to but may be practiced within the scope of the following claims.

13 I claim: 1. A method of permanently elongating strip which comprises:

(a) applying a tension force to the strip; and (b) constraining the strip while under tension vto at least one bend and at least one bend reversal which causes yielding and an incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental elongation strain is related to the applied tension force such: a

(1) that when the yielding occurs on alternate sides of the strip on successive bends the increment of elongation strain follows the equation and F r-i- R2 20'y R Rz in which F=tension force tistrip thickness ry=tensile yield stress ey=tensile yield strain Ae=increment of elongation strain, and R R =radii of successive bends. 2. A method of permanently elongating strip which comprises: V (a) applying a tension force to the strip; and (b) constraining the strip while under tension to at least one bend and at least onebend reversal which n causes yielding and an incremental elongation strain that is produced between abend and a subsequent bend reversal in which the magnitude. of incremental elongation strain is related to the appliedutension force such that when the yielding occurs on alternate sides of the strip on successive bends the incremen of elongation strain follows the equation per unit width of strip in which F=tension force'pe'r unit width of strip vy=tensile yield stress t=strip thickness sy=tensile yield strain Ae=increment of elongation strain, and R R .=radii of successive bends. 3. A method of permanently elongating strip which comprises:

(a) applying a tension force to the strip; and a (b) constraining the strip whileunder tension to at least one bend and at least one bend reversal which causes yielding and an incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental elongation strain is related to the applied tension force such that when yielding occurs on at least one side of the strip at a bend and on both sides of the strip at the subsequent bend reversal the increment of elongation strain follows the equation the increment of elongation strain follows the equation 1+ 2 1+ 2( 2 R 12 R112 1 ayt in which ey=yie1d strain t=strip thickness R =radius of bend R =radius of succeeding bend F=tension force per unit width of strip ay=yield stress. 5. A method of permanently elongating strip which comprises:

(a) applying a tension force to the strip; and (b) constraining the strip while under tension to at least one bend and at least one bend reversal which causes yielding and incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental elongation strain is related to the applied tension force such that when the increment of elongation strain follows the equation Y I in which e=yield strain t=strip thickness R =radius of bend R =radius of succeeding bend F=tension force per unit width of strip ay=yield stress. 6. A method of permanently elongating strip which comprises: i v (a) applying a tension force to the strip; and (b) constraining the strip while under tension to at least one bend and at least one bend reversal which causes an incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental strain elongation is related to the applied tension force such that when yielding occurs on only alternate sides of the strip on successive bends the increment of elongation follows the equation in which Ae=incremental elongation strain t=strip thickness R=radius of bend ey=yield strain F=tension force per unit width of strip ay=yield stress.

7. A method of permanently elongating strip which comprises (a) applying a tension force to the strip; and

(b) constraining the strip while under tension to at least one bend and at least one bend reversal which causes an incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental strain elongation is related to the applied tension force such that when yielding occurs on one or both sides of the strip at a given bend and on both sides of the strip at the subsequent bend the increment of elongation follows the equation F M in which Ae=incremental elongation strain R=radius of bend ey=yield strain F=tensi0n force per unit width of strip ay=yield stress. 8. A method of permanently elongating strip which comprises:

(a) applying a tension force to the strip; and

'(b) constraining the strip while under tension to at least one bend and at least one bend reversal which causes an incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental elongation strain is related to the applied tension force such that when Rey F the increment of elongation follows the equation it 4t F *[Fy- Fy 71191 in which F=tension force per unit width of strip ay=tensile stress t=strip thickness ey= tensile yield strain Ae=incremental elongation, and R=radius of bend when the bend radius equals the reverse bend radius. 9. A method of permanently elongating strip which comprises:

(a) applying a tension force to the strip; and

(b) constraining the strip while under tension to at least one bend and at least one bend reversal which causes an incremental elongation strain that is produced between a bend and a subsequent bend reversal in which the magnitude of incremental elongation strain is related to the applied tension force such that when E l t a'yt the increment of elongation follows the equation F Ae- 1)ey in which Roy F (Y+ E the increment of elongation strain will be Ae='yey,

in which F=tension force per unit width of strip R=bend radius ay=yield stress E=modulus of elasticity ey=yield strain Ae=increment of elongation strain =any numerical coefiicient greater than or equal References Cited UNITED STATES PATENTS 3,260,093 7/ 1966 Polakowski 72-163 2,180,879 11/1939 McFadden 72-183 2,059,993 11/ 1936 Hanson 72,205 1,975,846 10/1934 Hartmann 72164 FOREIGN PATENTS 1,028,5 37 5/1966 Great Britain. 655,444 7/ 1951 Great Britain.

OTHER REFERENCES Journal of The Iron and Steel InstituteBatty and Lawson, Heavy Plate Levellers; November 1965; pp. 1115-1123.

Iron and Steel EngineerBland and Alters; Tension 'Leveling; September 1967; pp. -105.

The Magazine of Metals Producing-Kusakabe and Hirasawa; Shape Improvement of Thin Steel Strip by Using the Roller Stretcher; December 1967; pp. 93-106.

RICHARD J. HERBST, Primary Examiner MICHAEL J. KEENAN, Assistant Examiner US. Cl. X.R' 

